Optimization of manifold design for 1 kW-class flat-tubular solid oxide fuel cell stack operating on reformed natural gas

Journal of Power Sources 327 (2016) 638e652

Contents lists available at ScienceDirect

Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour

Optimization of manifold design for 1 kW-class flat-tubular solid oxide fuel cell stack operating on reformed natural gas Kashif Rashid a, b, Sang Keun Dong b, a, *, Rashid Ali Khan a, b, Seung Hwan Park c a

Energy System Engineering, Korea University of Science and Technology (UST), 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea Advanced Combustion Laboratory, Korea Institute of Energy Research (KIER), 152 Gajeong-ro, Yuseong-gu, Daejeon 34129, Republic of Korea c STX Heavy Industries Co. Ltd, 533 Dalseo-daero, Dalseo-gu, Daegu, Republic of Korea b

h i g h l i g h t s
CFD tools are utilized to optimize the manifold design for FT-SOFC stack.
Remodeled manifold showed improvement in flow uniformity and pressure drop.
Electrochemical and internal reforming modeling applied on 1 kW FT-SOFC stacks.
Developed manifold stack exhibited uniform distributions.
Developed manifold stack demonstrated an enhanced stack output power.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 24 February 2016 Received in revised form 13 July 2016 Accepted 21 July 2016 Available online 3 August 2016

This study focuses on optimizing the manifold design for a 1 kW-class flat-tubular solid oxide fuel cell stack by performing extensive three-dimensional numerical simulations on numerous manifold designs. The stack flow uniformity and the standard flow deviation indexes are implemented to characterize the flow distributions in the stack and among the channels of FT-SOFC's, respectively. The results of the CFD calculations demonstrate that the remodeled manifold without diffuser inlets and 6 mm diffuser front is the best among investigated designs with uniformity index of 0.996 and maximum standard flow deviation of 0.423%. To understand the effect of manifold design on the performance of stack, both generic and developed manifold designs are investigated by applying electrochemical and internal reforming reactions modeling. The simulation results of the stack with generic manifold are validated using experimental data and then validated models are adopted to simulate the stack with the developed manifold design. The results reveal that the stack with developed manifold design achieves more uniform distribution of species, temperature, and current density with comparatively lower system pressure drop. In addition, the results also showed ~8% increase in the maximum output power due to the implementation of uniform fuel velocity distributions in the cells. © 2016 Elsevier B.V. All rights reserved.

Keywords: Flat tubular solid oxide fuel cell Flow uniformity Manifold optimization Computational fluid dynamics calculations Electrochemical reaction Stack performance

1. Introduction The solid oxide fuel cell (SOFC) is a promising and attracting device that produces electricity with higher efficiency, lower emissions of greenhouse gasses, and extremely low noise pollution. It is a device that converts fuel directly into electricity through electrochemical reactions without combustion. Due to their fuel

* Corresponding author. Advanced Combustion Laboratory, Korea Institute of Energy Research (KIER), 152 Gajeong-ro, Yuseong-gu, Daejeon 34129, Republic of Korea. E-mail address: [email protected] (S.K. Dong). http://dx.doi.org/10.1016/j.jpowsour.2016.07.077 0378-7753/© 2016 Elsevier B.V. All rights reserved.

flexibility, they can be operated on all carbonaceous fuels including natural gas, biogas, pure hydrogen, methanol [1]. The SOFC's generally are categorized into three types, namely, planar, tubular and flat tubular. Planar-type SOFC design has superior characteristics in terms of their power density due to the more effective current collection by a planar interconnector. In contrast, tubular SOFC systems have superior characteristics to planar SOFCs regarding their thermal and mechanical properties. However, the flat-tubular SOFC (FT-SOFC) possesses the positive features of both planar and tubular SOFC. In the FT-SOFC, the ribs inside the porous electrode channels allow electronic movement thus shortening electronic path and improving electrical power [2e4].

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

To get higher power output from the SOFC, the cells are arranged in stacks, and it is essential that the fuel is supplied uniformly to the channels of each cell to obtain satisfactory performance of the stack [5,6]. The non-uniformity of the reactants inside the electrodes due to inefficient design will lead to fluctuations in stack performance because of non-homogeneous local current density and cell voltage. Another drawback of fuel flow non-uniformity is that it produces temperature gradient along the length of the cell due to different rates of the electrochemical reaction in different regions. The temperature gradient causes thermal stresses within the individual cells, ultimately leading to severe degradation of stack performance [7,8]. In addition, chemical, electrochemical reactions, as well as the electrical and ionic conductions of the electrodes and electrolyte are affected by the local temperature variations. Hence, an appropriate manifold design is imperative to get satisfactory performance from the SOFC stack. The uniformity of flow in the stack can be ensured by designing manifold in such a way that the pressure variations from the inlet manifold to the outlet are small as compared to the gas channels of the individual cells. It is a fundamental consideration for system design that overall pressure drop should be as low as possible to avoid the use of an external device like blower or compressors [5,9,10]. To investigate the effect of different design parameters, a computational approach is always advantageous over experimental since it significantly reduces the cost, time and efforts, and allows an easier way to explore the various parameters in much detail [9,11,12]. Over the last decade, a number of models and fuel cell stack designs have been suggested and numerically analyzed for flow uniformity. Boersma and Sammes proposed an analytical model to work out the pressure and flow distributions in SOFC stack [13]. Huang et al. studied the effect of different flow distributions and flow uniformity on the cell performance [14]. Winkler et al. compared the flow distributions of the planar, tubular and ring tubular fuel cell stack using theoretical approach [15]. Xia et al. studied the flow characteristic in SOFC stack by coupling the momentum, energy, continuity and transfer equations and found that co-flow configuration is more suitable to obtain uniform temperature and current distributions than the counter-flow arrangement [16]. However, in the recent years, many researchers have devoted their attention towards the design and optimization of the external manifold to obtain a uniform flow through all the channels of the SOFC stack. Sung et al. derived a mathematical model for Z-type and U-type manifold configurations to distribute the reactants among the channels within bipolar plates. They explored specific designs that satisfy the derived manifold equations for each formation along with the static pressure distribution inside the manifold [17]. Similarly, Chen et al. adopted CFD approach to study the pressure variations and flow distribution in fuel cell stack manifold. They presented momentum-balance theory and pressure drop model to explain the physical mechanism of flow distribution. Their results revealed that both the channel resistance and the manifold width can enhance the uniformity of the flow distribution [18]. Tong et al. identified geometric strategies and used 2D numerical simulation to obtain identical outflows through all exit channels. They employed standard deviation from uniformity technique to identify the degree of mass outflow uniformity through each port [19]. Kee et al. adopted a 2D model with laminar flow in the cells and presented a design that showed the relationship between the flow distribution uniformity and the design parameters. The key parameter responsible for the flow uniformity was still not pointed out [10]. In an effort to understand the major factors related to flow uniformity in the manifolds, Wuxi Bi et al. performed CFD calculations for the flow uniformity in planner SOFC stack using 3D

639

modeling with real geometric and operational parameters. They concluded that the ratio of the outlet width to the manifold inlet width (a) is a key design parameter which affects the flow uniformity [11]. Chen et al. executed 3D gas flow CFD calculations for 10cells modular planar SOFC stack to optimize the manifold. They employed a combination of alternative manifold layouts for the fuel and air, inlet/outlet manifold positions, and different radii to explore best possible manifold configuration [5]. Su et al. also performed 3D flow distribution analysis for 10-cells planar SOFC stack with different rib arrangements. The stack flow uniformity and standard flow deviation indexes were implemented to illustrate the flow distribution qualities in the stack and among the rib channels [9]. In the early studies, generally, the planar SOFC's stacks were considered for analysis of fluid flow or occasionally both for flow and electrochemical analysis [5,8,9,11,20]. Most of the research were focused on analyzing the hydrodynamic models or electrochemical phenomenon separately but did not study both the models together. The studies that involved both the numerical and analytical analysis were only for flow analysis; tends to improve pressure and flow distributions in the cells of the stack [10,11,13,21e23]. Their analysis did not consider the effect of electrochemical reaction, species and temperature distributions. There are some models found in the literature which integrates the flow analysis, electrochemistry and heat transfer together but are generally confined to the single cell [16,24e26]. In the present study, three-dimensional (3D) numerical and experimental analysis are performed on 1 kW-class FT-SOFC stack fueled by reformed natural gas. This work consists of two parts; the first part only deals with the hydrodynamic analysis of different manifold configurations to identify an optimal manifold design capable of delivering the uniform mass flow rate to the channels of all the cells in the FT-SOFC stack. In the second part, electrochemical and internal steam reforming modeling is implemented on the 80 cells FT-SOFC complete stack integrated with the manifold. The generic manifold design and the best manifold designed determined by the numerical analysis are simulated to study the full-scale operation of the stack with reformed gas mixture. The effect of manifold design on the flow uniformity, temperature, species and current density distributions, and stack performance has been explored in depth. 2. Experimental setup Fig. 1 shows experimental equipment's of SOFC stack with necessary balance of plant (BOP) system within the hot box. The system consists of a steam reformer, heat exchangers, 80 anode supported FT-SOFC's stack mounted over manifold and startup burner. A U-shape steam reformer along with steam generating tube is embedded in the combustion chamber to convert the natural gas into reformed gas mixture. A startup burner is installed inside the hot box at a location beneath the reformer. Heat exchangers are positioned on both sides of the stack. These heat exchangers utilize the heat energy of exhaust products from the combustion chamber to preheat the incoming cathode air. For operating the system, first startup burner was fed with 1.2 L min1 of natural gas to heat up the system components. Once the reformer inlet temperature reached around 650  C, reforming process was initiated by injecting 3.7 L min1 of natural gas with 8 ccm (10 L min1) of water. The steam to carbon ratio (s/c) was maintained at 2.8. The reformed natural gas was fed into the manifold and at the same time, pre-heated air from the heat exchangers enters into the stack enclosure. When the stack temperature reached and stabilized at 760  C, an external load was connected to measure the stack voltage for a current range of

640

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

Fig. 1. Experimental setup (a) Hotbox with necessary instrumentations (b) FT-SOFC 80 cells stack (c) Schematic diagram with transmitter positions.

0e19.08 A. The output voltage was recorded for each of the corresponding current drawn once the system got stabilized. The startup burner was turned off when system switch to normal operating mode, meanwhile, unreacted anode fuel and cathode air were burnt in the combustion chamber to deliver necessary heat to the reformer for steady reforming operation. The system was operated at normal operating mode for continuous 2000 h, and corresponding data was collected. The results are demonstrated and discussed in subsequent sections. 3. Description of manifold designs An isometric diagram of FT-SOFC stack is presented in Fig. 2(a). The stack consists of 80 cells divided into 4 groups each containing 20 cells placed vertically in a pre-heated air enclosure. The reformed natural gas is supplied to these cells with the help of manifold attached at the bottom. The objective of the current study is to carry out design optimization of the manifold design to ensure that fuel supplied to each cell channel is uniform to get even current distribution and diminish the temperature gradients, to extend stack life. The manifold designs that have been simulated are broadly divided into two schemes. In the first classification, the generic manifold design is parametrically varied. In the second layout, the generic manifold is remodeled to achieve better effluent uniformity. The descriptions of these manifold designs are presented below. 3.1. Generic manifold design The 3D mechanical design of generic manifold that is numerically examined in the present study is shown in Fig. 2(b). Fluid domain along with the dimensions of the manifold is presented in Fig. 2(c). The fuel enters through a single hole, travels through the

manifold then move upward through the opening between manifold and chambers, and finally discharge into the anode channels. 3.2. Parametric variations in generic manifold design 3.2.1. Variable manifold inlet diameters (4) The first variation in the design of the generic manifold study is to explore the effect of manifold inlet diameter on the mass flow uniformity. In this configuration, the diameter is increased to reduce the inlet velocity to attain better flow distribution inside the manifold. In the present case, manifold inlet diameter is varied from 11 to 14 mm. 3.2.2. Linear tapered manifold The linear tapering design of manifold is presented in Fig. 2(d). It is expected that downstream flow in the manifold chambers will be diminished gradually because of mass extraction by each anode electrode channels. If the height of the manifold were to remain same throughout the length, the axial momentum would subside steadily. Because of this momentum decrease, static pressure would increase progressively. This increase in static pressure will tend to promote higher flow through the downstream openings to the chambers [19]. The generic manifold is tapered for the height of 6 to 10 mm to handle this trend. 3.2.3. Perforated sheet inside manifold The manifold with the perforated sheet is shown in Fig. 2(e). In this configuration, a perforated sheet is fixed at the middle of the manifold. The diameter of holes on the sheet is altered from 2.5 to 4.5 mm to vary the flow rate in the last chambers, keeping manifold inlet diameter fixed at 11 mm. As the 80 cells are vertically positioned over the 4 chambers of the manifold; the probability is

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

641

Fig. 2. (a) 3D CAD design of generic manifold with 80 cells stack place in air enclosure. (b) 3D mechanical design of generic manifold. (c) The fluid domain of generic manifold with required dimensions. (d) Linear tapering of the generic manifold. (e) Perforated sheet placed at the center of the generic manifold. (f) 3D mechanical design of remodeled manifold. (g) The fluid domain of remodeled manifold with required dimensions. (h) Remodeled manifold without diffuser inlets.

that the 40 cells in the first two chambers will receive a higher amount of fuel than the last 40 cells. The idea of placing perforated sheet inside the manifold is to increase the flow rate in later chambers so that all 80 cells should also receive identical mass flow rates.

3.2.4. Remodeling generic manifold with diffuser inlets The 3D design of remodeled manifold is presented in Fig. 2(f). It consists of the manifold, diffuser, diffuser inlets, openings between diffuser and chambers, chambers and the exit ports. The fuel enters the manifold through two inlets, loses some momentum inside small manifold section, and travel towards diffuser through the diffuser inlets. Fuel then enters the chambers from the openings at the top of the diffuser and leaves the exit ports. The flow extracted domain along with dimensions of the remodel manifold is provided in Fig. 2(g). The manifold inlet diameter (4) is varied from 11 to 15 mm to quantify their effect on the flow uniformity while the diffuser inlets diameter is fixed at 3 mm.

3.2.5. Remodeled manifold without diffuser inlets and variable diffuser front The schematic diagram of remodeled manifold without the diffuser inlets is shown in Fig. 2(h). In this design, fuel enters directly from the manifold into the diffuser through diffuser front. Only the height of diffuser front is varied from 5 to 8 mm during the course of simulation while other dimensions are kept remain unchanged.

4. Manifold CFD calculations 4.1. Governing equations In this section, numerical calculations are only performed on the generic and different proposed manifold designs. These calculations are based on isothermal condition, without considering electrochemical reactions. The gas transport processes that are occurring inside manifold can be described by continuity and

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

momentum conservation equations [5]: Continuity equation:

0

mi ¼ mi

V$ðr! vÞ¼0

(1)

Momentum equation:

V$ðrmix ! v ! v Þ ¼ VP þ V$t

(2)

Where ! v the velocity vector of mixture gas, P is working pressure, t is the stress tensor and rmix is the density of the mixture, which can be estimated by utilizing ideal gas state equation:

rmix ¼

PMmix RT

(3)

Where R is a universal gas constant, T is the operating temperature (1033.15 K) and Mmix is the molar mass of the fuel gas mixture, which can be calculated as:

Mmix ¼

N X

xi Mi

(4)

i¼1

Where xi and Mi are the mole fraction and molar mass of the species i respectively. The viscosity of the gaseous fuel can be evaluated by ideal mixing law as [27]:

mmix ¼

XN

xi m i i¼1 PN j¼1 xj ∅i;j

(5)

Where, ∅i;j is a dimensionless number acquired from:

mi mj

!1 2 =

!1 2 2 41 þ

Mi Mj

!1 4 32 5 =

=

1 M ∅i;j ¼ pffiffiffi 1 þ i Mj 8

(6)

Where N is the total number of species in the mixture, xi, xj are the mole fractions of species i and j and Mi, Mj are the molecular weights of the species i and j. mi is a dynamic viscosity determined by Sutherland's law using the kinetic theory of gases.

 1:5

mi T z T mi

T þ Si T þ Si

.XN m i i¼1 N

(9)

The stack flow uniformity index U varies between 0 and 1. The higher the value of U, more uniform is the stack flow distributions. To achieve manifold design flow optimization, the value of U should be close to 1 with viable low-pressure drops in manifold [11]. To check the flow distribution quality at the individual cell level, standard flow deviation index is used to distinguish the flow among the anode channels. The minimum gas flow rate criteria for stack may not determine the whole stack performance alone. So, it is very important to maintain uniform distribution among all the anode channels to get even current distribution and diminish the temperature gradients, to extend the stack life. The standard flow deviation index (G) can be calculated by following expression [9,14]:

1  1 XNc ðui  uÞ 2 2 i¼1 Nc u

 G¼1

=

642

(10)

Where Nc ¼ 21 the number of anode channels in a single cell is, ui is the velocity at the ith channel and u is the average velocity. 4.3. Mesh generation The quality of the mesh is one of the most important aspects of CFD calculations. To save the computational time, only half of the manifold designs mesh for flow analysis. The Ansys® ICEM CFD is used for making hexahedral elements for all the manifold designs. The non-conformal mesh strategy is used to mesh all parts of manifold separately then these individual parts are combined in the solver [28]. The finer mesh is made where the sharp deviation in flow distribution is expected. The grid independence is also tested for the generic manifold to investigate the accuracy of the numerical solution. The simulations with two different mesh sizes of 2.5 million and 4.0 million elements were run. The flow uniformity indexes are 0.826 and 0.828 for 2.5 and 4.0 million meshes respectively. Whereas normalized flow showed similar results which clearly indicate mesh independence. The rest of flow calculations were performed with meshes of about 2.5 million nodes. The generic manifold with hexahedral mesh elements is presented in Fig. 3.

(7) 4.4. Boundary conditions



mi , T ; Si are the reference values of viscosity, temperature and

Sutherland constant. The parameters for viscosity calculation can be found in Ref. [27]. The calculated viscosity of reformed gas mixture is 1.7894 kg m1s1.

4.2. Criteria for stack flow uniformity As mentioned earlier, present FT-SOFC's in the stack are placed vertically over manifold in parallel. It is anticipated that all cells should consume the same amount of fuel to produce the same amount of electric current. Thus, the overall performance of the stack is influenced by the individual cell that receives a minimum amount of fuel. The stack flow uniformity index (U) is used to illustrate the mass flow distribution among the connected cells [11].

 0 0  U ¼ min mi : mN 0

0

To solve the mathematical model, three types of boundary conditions are used: (i) The mass flow inlet boundary condition is applied at the inlet of the manifold. The output of the reformer (1.96134e5 kg s1 reformed gas) is directed at the inlet of the manifold (ii) The pressure outlet boundary condition is applied to all the outlet ports of the manifold and gauge (reference) pressure of 0 Pa is set (iii) All other walls are treated as adiabatic, stationary wall and shear condition as no slip (iv) Symmetry boundary condition is applied, and only half of manifolds are simulated

4.5. Solver settings

(8)

Where mi and mN are the normalized mass flow received by the ith and Nth cells. These mass flow rates can be normalized using following expression:

All the necessary parameters to implement flow analysis of manifold designs are presented in Table 1. The commercial software Ansys® Fluent is employed to carry out the numerical simulations. The governing equations are solved through finite volume

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

643

To further investigate the flow characteristics within the manifold, a full manifold with velocity vectors and pathlines distributions are shown in Fig. 4(b). As the fuel enters the manifold from the center, it travels straight through, collides with the manifold back wall forming stagnant flow zone. This zone has a major influence towards the bottom wall. As the central flow of manifold diverts toward the opening of the chambers, a recirculation zone is formed near the back wall of manifold [29]. It is important to note that velocity distribution is strongly driven by the shear effect of the central manifold flow. The fluid becomes relatively streamline near the entrance, causing higher outflow through the first 20 cells. The similar recirculation takes place in the middle of the manifold. These re-circulations are making local velocity distributions non-uniform, and these flows phenomenon are marked in Fig. 4(b). The effluent flow division into two segments, emphases the importance to improve this generic manifold design so that all the cells mounted on the chambers of the manifold should receive identical mass flow rate.

5.2. Effect of parametric variations in generic design In the subsequent section, numerical results of geometric parameterization on the generic manifold include variable manifold inlet diameters, linear tapering of the manifold and perforated sheet in the manifold are presented. Fig. 3. Grid quality for the generic manifold.

approach. The pressure based solver is selected; steady state analysis is performed using 2nd Order Upwind schemes for all parameters. The minimum absolute convergence on the residual scale is set to 106 for all parameters. 5. Results and discussion 5.1. Flow distributions of generic manifold Fig. 4(a) shows normalized mass flow distribution for 40 cells generic manifold. In this figure, two trends can be seen. The normalized mass flow of first 20 cells is higher than the last 20 cells. There are couples of reasons for this behavior; (a) first 20 cells are closer to the manifold inlet, receiving a higher amount of fuel (b) secondly, 40 cells are separated by 34 mm distance. Therefore, there is a decline of flow in last 20 cells. To further illustrate these flow segmentations into two groups, the velocity magnitude contours at the selected manifold exit ports are displayed in Fig. 4(b). The reduction in effluent flow to the anode channels can be clearly seen from the first chamber to the last chamber. The flow uniformity index (U) for this manifold design is 0.826 which is acceptable for low fuel utilization [11].

5.2.1. Variable manifold inlet diameter (4) To reduce the flow non-uniformity in the two compartments of the manifold, inlet diameter of the manifold (4) is varied to evaluate their effect on flow distribution. Fig. 4(c) shows the effect of different manifold inlet diameters on the normalized fuel mass flow with constant fuel supply for 40 cell stack manifold. For the case where inlet diameter is 11 mm, a considerable difference in the fuel flow rate is observed between the first and last 20 cells. Therefore, it is found least uniform, having uniformity index of U ¼ 0.826. As presented in Fig. 4(c), the difference of normalized mass flow received between the first 20 cells, and last 20 cells are decreasing with the increase of manifold diameter. The reason behind this behavior is that, as the diameter of manifold inlet increases, the fuel velocity reduces at the inlet as the total fuel inlet supply is unchanged. Thus, pressure drop at the inlet of the manifold decreases while pressure drop increases in the effluent to the chambers. This decline in pressure drop at the manifold inlet redistributes the fluid flow and is a major reason for the decrease of difference in the amount fuel received by the cells of two manifold chambers [5]. It is quite evident from Fig. 4(d) that diameter of the manifold inlet is a major factor for the flow uniformity of manifold design. The uniformity index is increased from 0.826 to 0.953 when the diameter of the manifold inlet is increased from 11 mm to 14 mm.

Table 1 Operating parametersa. Operating temperature (K) Operating pressure (Pa) Operating current density (A m2) Fuel inlet (kg s1) Air inlet (kg s1) Reformed gas (mass fraction) H2/H2O/CH4/CO/CO2 Cathode air (mass fraction) O2/N2 Effective gas diffusion coefficients (m2 s1) H2/H2O/CH4/CO/CO2/O2/N2 a

Calculated parameters from STX operated stack.

1033.15 101325 2523.8 1.96e4 3.23e3 0.082/0.4322/0.0487/0.17/0.2671 0.233/0.767 4.73e5/1.20e5/1.97e5/1.74e5/1.41e5/1.27e5/1.30e5

644

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

Fig. 4. (a) Normalized mass flow distributions for 40 cells generic manifold. (b) Flow distributions and velocity magnitude at selected manifold exit ports (c) Effect of variable manifold inlet diameters (4) on normalized mass flow distributions of the generic manifold. (d) Uniformity index function of variable manifold inlet diameter. (e) Effect of linear tapering on effluent mass flow rate. (f) Velocity vector and Stream/pathlines distributions for fuel flow. (g) Effect of the perforated sheet with variable holes sizes on normalized mass flow distributions. (h) Velocity vector and Stream/pathlines distributions for fuel flow.

5.2.2. Effect of linear tapered manifold on flow uniformity The second design modification presented here is the linear tapering of the manifold cross-sectional area. The main purpose of using the tapering technique is to reduce the height of manifold along the flow direction in order to diminish the effect of any increase in pressure due to the drop in axial momentum [19,30]. Fig. 4(e) shows the effect of variation in the manifold cross-

sectional area on the normalized mass flow rate. All tapering heights show improvement in the flow uniformity in comparison to generic manifold design. The normalized mass flow rate for the last 20 cells progressively decreases for tapering height of 9 mm and 10 mm, whereas, for tapering heights (6, 7, and 8) mm, the amount of fuel received by the last 20 cells increases and even superseded the first 20 cells. The reason is that height of manifold back side is

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

being reduced gradually than the fuel entrance side. The fluid velocity is increasing steadily because of reduced cross-sectional area of the manifold in the streamwise direction. Below 8 mm of tapering height, normalized mass flow received by the last 10 cells increases sharply while uniformity index is observed to decline because of reduced cross section causing higher outflow. It is apparent from Fig. 4(e) that best uniformity index is found between 8 and 9 mm height. To visualize the effect of tapering technique on flow distribution, velocity vector and pathlines distributions of 8 mm height tampering are displayed in Fig. 4(f). It is evident from Fig. 4(f) that fluid flow is more streamlined than the one revealed in Fig. 4(b). The highest flow uniformity achieved by using tapering approach is 0.974 for the tapering height of 8 mm. 5.2.3. Effect of perforated sheet inside manifold on flow uniformity The numerical results are shown in Fig. 4(a) for the generic design of manifold disclosed that there are two distinct divisions in the normalized mass flow of the first 20 and last 20 cells. The lack of mass flow in the back end of the manifold chamber is counteracted

645

by the use of the perforated sheet. The simulated results of the manifold with variable holes diameters on the sheet are presented in Fig. 4(g). There is a noticeable improvement in the flow uniformity for all the diameters of the sheet holes except for diameter of 2.5 mm. The 2.5 mm diameter of sheet hole is too small, and it further increases the resistance to flow to the last chamber of the manifold which resulted in worst flow uniformity of 0.732. The prominent feature in Fig. 4(g) is that normalized mass flow received by the last 20 cells superseded first 20 cells for a hole diameter of 4.0 mm and 4.5 mm. The reason is that fluid after passing through the sheet holes confronts extreme hindrance to return by the upstream flow plus the wall of the sheet. These results are further elaborated with the assistance of Fig. 4(h) that shows the velocity distributions inside the manifold with 4.0 mm hole diameter. The related problems with this strategy are the increase of pressure drop (i.e. 20.4 Pa whereas it is 18.03 Pa in the case of generic design) and localized turbulence at the inside wall of perforated sheet. The best uniformity index of 0.977 is achieved for sheet holes with a diameter of 4.0 mm beyond this hole size, decline in the mass flow

Fig. 5. (a) Effect of variable manifold inlet diameters (4) on normalized mass flow distributions of remodeled manifold. (b) Velocity vector and Stream/pathlines distributions for fuel flow. (c) Effect on normalized mass flow distributions of remodeled manifold without diffuser inlets. (d) Velocity vector and Stream/pathlines distributions for fuel flow. (e) Effect on normalized mass flow distributions of remodeled manifold without diffuser inlets. (f) Flow distributions and velocity magnitude at selected manifold exit ports.

646

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

uniformity is observed. 5.3. Remodeled manifold with diffuser inlets (variable manifold inlet diameter) The effect of variable manifold inlet diameter on the normalized mass flow received by the individual cell is shown in Fig. 5(a). It is apparent from Fig. 5(a) that mass flow distribution is adversely affected by this remodeling of manifold despite the increase of manifold inlet diameter. The mass flow distributions for all manifold inlet diameters found similar, and there is a clear division in mass flow rates between first 20 and last 20 cells. In this remodeled manifold, when fluid enters the diffuser from diffuser inlets, it regains part of lost momentum due to the smaller cross-section. Because of higher velocity and low static pressure at the diffuser front, normalized flow received by the first 20 cells is low compared to last 20 cells which are quite cleared in Fig. 5(a). There is an increased static pressure at diffuser back due to a gradual increase in the cross section of the diffuser which reduces fluid axial momentum. This increased static pressure impels higher effluent mass flow through the last 20 cells. To envision the flow distribution in this remodeled manifold, velocity and pathlines are presented in Fig. 5(b). The flow is least streamwise, and numerous recirculation zones are generated marked in the figure. The increased velocity at the diffuser front and the formation of recirculations zones are the reasons for this flow non-uniformity. 5.4. Remodeled manifold without diffuser inlets (variable manifold inlet diameter) It is cleared from the previous discussion that the use of diffuser inlets for the remodel manifold design has an adverse effect on the flow uniformity. In this section, the numerical results of remodeled manifold without diffuser inlets are discussed. Fig. 5(c) shows normalized mass flow rate received by the individual cells. It reveals that there is a significant improvement of flow uniformity without diffuser inlets for all manifold inlet diameters. There is a minor difference of mass flow rates in the first 20 cells and last 20 cells. To inspect this significant improvement of flow uniformity, flow distributions are presented in Fig. 5(d). It is evident from the figure that the flow is more streamlined inside the diffuser with less escalation in the momentum at the diffuser front in comparison to Fig. 5(b). Because of the reduced velocity at the diffuser front, the effect of the rise in static pressure at the diffuser back is small as compared to Fig. 5(b). The recirculation is only observed near the diffuser back wall causing higher pressure drops near the upper wall of diffuser [29]. Because of this recirculation and higher pressure drop, the lower effluent flow rate is observed from the last chamber which can be seen in Fig. 5(c). However, the flow uniformity indexes show little dissimilarity with the cross section of the manifold inlet. The highest uniformity index of 0.995 is obtained for manifold inlet diameter of 13 mm. 5.5. Remodeled manifold containing without diffuser inlets (variable diffuser front) Another important parameter of remodeled manifold design is the height of the diffuser front. The results of numerical computations are displayed in Fig. 5(e) that shows the effect of diffuser front height on the normalized flow rate of each 40 cells. It is cleared from Fig. 5(e) that the height of the diffuser front 5 mm and 6 mm has the highest uniformity indexes with a minimum of mass flow rate variations in the first and last 20 cells. Beyond, the diffuser front height of 6 mm, there is a considerable decline in the flow uniformity is observed. In addition, the difference in mass flow

received by the cells in the two chambers starts to increase. As the height of the diffuser front increases, some of the fuel streams which is above the centerline passes straight through the main diffuser with higher velocity without losing any momentum. Because of this higher inlet velocity and low static pressure at the diffuser front, the effluent mass flow through first 20 cells is lower, whereas, at the diffuser back, dynamic pressure is being converted into static pressure which causes the increased flow through the last 20 cells. The highest uniformity index 0.996 is achieved for diffuser front of 6 mm, and the flow distributions for this design are presented in Fig. 5(f). The figure clearly reveals that the flow after entering the diffuser is mostly streamlined with very few recirculations at the diffuser back. This is further elaborated with the help of contours for velocity magnitude at selected exit ports of remodeled manifold with 6 mm diffuser front which are shown in Fig. 5(f). Fig. 5(f) clearly exhibits that there is no disparity of effluent flow to the chambers and exit ports which is a clear indication that appropriate uniformity has been achieved. 5.6. Comparison of generic manifold and remodeled manifold with the highest uniformity A brief summary of manifold designs with their calculated uniformity indexes is reported in Table 2. It is evident from above flow analysis and stated results in Table 2 that remodeled manifold with 11 mm diameter, 2 fuel inlets, and 6 mm of diffuser front is the best among all the presented designs. In this section, comparison of some of the major features of the generic manifold and remodeled manifold with the highest uniformity is presented. The first performance measure discussed here is the standard flow deviation index. Fig. 6(a, b) shows the variations in normalized flow received by individual anode channels of cells 1, 10, 20, 21, 30 and 40 for generic and best-identified manifolds respectively. The noticeable attribute of the generic manifold is that mass flow received by individual channels of selected cells follows a pulsating trend except for the channels of cell 10 and 30 which show fewer fluctuations. In addition, the flow is relatively more uniform among the channels 6 to 18. The reason is that fuel enters from the center of the manifold, after colliding with the back wall of manifold it returns along the side walls while chambers are positioned 10.5 mm away from the centerline. Therefore, the channels at the outer sides of cells are most affected by these uneven flow distributions. The two major zones were observed where re-circulations were being taken place; the reason of these recirculations was explained in section 5.1. These re-circulations are the main source of uneven distributions. This phenomenon in macro-scale is presented in Fig. 4(b). The flow distribution characteristics among all the single channels are defined by the position of manifold inlet and outlet [9]. Thus, the maximum deviation of 0.5074 and 0.637 is observed in cell 1 and cell 40 respectively which is displayed in Table 3. In comparison, remodeled manifold shows better flow uniformity even at anode channels level, the lowest normalized mass flow received by any individual channel is above 0.993 which is a clear indication that identical flow distribution among the channels has been achieved. The maximum deviation is of 0.423%, and 0.418% is observed for the cell 10 and 30 which lies at the center of the chambers. In this design there are two fuel inlets; fluid velocity is highest along the flow direction, underneath the channels from 4 to 18. The fluctuations in normalized flow received are prominent especially for cell 10 and 30 because of the high flow region at the center and lower towards the side walls. The second feature is the drop in pressure suffered by the flow along the manifold. In this regards, remodeled manifold offer an overall pressure drop of 7.51 Pa in comparison to 18.03 Pa. The less pressure drop is helpful in reducing the operating cost of the BOP. The pressure distributions of both the designs are

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

647

Table 2 Summary of manifold designs with uniformity indexes. Manifold designs

Generic manifold

Generic manifold with manifold inlet diameter (4 ¼ 14 mm)

Generic manifold with tapering width (8 mm)

Generic manifold with perforated sheet with holes (4 ¼ 4.0 mm)

Remodeled manifold with diffuser inlets (4 ¼ 11 mm)

Remodeled manifold without diffuser inlets (4 ¼ 13 mm)

Remodeled manifold without diffuser inlets, with 6 mm diffuser front

Uniformity indexes (U)

0.826

0.953

0.974

0.977

0.639

0.995

0.996

Fig. 6. The distribution of normalized mass fuel flow among the anode channels of selected cells (a) generic manifold (b) best numerically identified manifold. The static pressure distributions of (c) generic manifold (d) best numerically identified manifold.

displayed in Fig. 6(c, d). In the subsequent part of this manuscript, the generic manifold is assigned as reference manifold and best identified manifold is designated as developed manifold design respectively. 6. Numerical calculations of full 80 cells stack with manifolds In this section, numerical simulations are performed on full 80 FT-SOFC's 1 kW stack with reference and developed manifold designs to establish their effects on the stack performance. The internal steam reforming (ISR) modeling and electrochemical reaction (ECR) modeling are included in the numerical calculations. The reformed gas mixture is supplied at the manifold inlet (for gas composition see Table 1), to generate power. The computational domain and working mechanism are shown in Fig. 2(a). The physical properties necessary to run the simulation are provided in Table 4. Due to the presence of methane and carbon mono oxide in the fuel stream, internal steam reforming (ISR) and water gas shift reactions (WGSR) take place at the catalyst layer of the anode

Table 3 The standard flow deviation index. Cell number

1 10 20 21 30 40

Generic manifold

Remodel manifold with 6 mm diffuser front

Deviations (%)

Deviations (%)

0.5074 0.249 0.448 0.421 0.1095 0.637

0.198 0.423 0.2036 0.2038 0.418 0.197

electrode, supplementing further hydrogen in the fuel stream. The chemical reactions taking place at the anode electrode are as follows:

CH4 þ H2 O /CO þ 3H2 CO þ H2 O /CO2 þ H2

ðISRÞ

(11)

ðWGSRÞ

(12)

648

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

Table 4 Physical properties of cell componentsa.

Density (Kg m3) Specific heat (J Kg1 k1) Thermal conductivity (W m1 k1) Porosity (ε) Average particle diameter (dp) Tortuosity (x) Thickness (mm)

Cathode electrode

Electrolyte

6864 607 10 35 2.5 2.9 20

5950 400 2.7 e e e 10

Data obtained from STX Daegu, South Korea.

The hydrogen molecules and oxygen ions available at the interface of anode-electrolyte react to produce steam and releases electron that transported to the cathode via current collector to produce electricity.

H2 þ O2 /H2 O þ 2e 0:5O2 þ 2e /O2

ðReaction at anodeÞ

ðReaction at cathodeÞ

(13) (14)

The electrochemical oxidation of CH4 and CO is not considered because the rate of ISR and WGSR reactions are much faster than the electrochemical reaction [31,32]. The related equations for ECR modeling are summarized in Table 5. The mathematical model provided by Costamagna et al. for the calculation of activation polarization is used [33]. To solve Butler-Volmer equation, the preexponential factor and activation energies of anode and cathode are opted from Suzuki et al. [34]. The chemical model suggested by Lehnert et al. [35] for the calculation of ISR and WGSR rates are employed, and their model equations are presented in Table 6. To calculate the binary diffusion coefficient, the equation presented by Hirscherfelder et al. [36] is adopted. Whereas to calculated the diffusion of gas through porous media, Knudsen equation is used [36]. The effective diffusion

coefficients of individual species in a reformed gas mixture that includes both the effect of binary and Knudsen diffusions are displayed in Table 6, and the calculated effective diffusion coefficients of all the species are provided in Table 1. In the case of SOFC, various processes are taking place simultaneously which include fluid flow, mass and heat transfers as well as ECR's and chemical reactions. The CFD calculations are implemented under the assumption of steady state, laminar and incompressible flow. The governing equations for continuity, momentum, energy and species along with their source terms are presented in Table 7. The finite volume approach is adopted to discretize the differential equations and commercial software Ansys® Fluent is employed to solve the governing equations. All the boundary conditions used in previous sections are applied except for symmetry condition. The species transport model along with diffusion phenomenon is used in the solver whereas ECR modeling and ISR reaction rates are incorporated in the solver with the in-house UDF written in C language. All the equations are solved for 2nd order accuracy with convergence criteria on the residual scale is set to 103 for continuity, momentum, and species whereas 106 for energy equation.

Table 5 Governing equations for electrochemical reaction modeling. Cell voltage

VCell ¼ Erev  IRirr ¼ Erev  IðRact þ Rohm Þ  hconc

Nernst potential (OCV)

Erev ¼ E þ RT 2F ln

Ohmic losses

san ¼ 9:510 exp T

PH2 ðPO2 Þ0:5 PH2 O



7



1150 T

se ¼ 3:34  104 exp Activation overpotential

Concentration overpotential

1 Ract an

¼ gan

1 Ract ca

¼ gca

  2F RT

PH2 P

 

PO2 P

4F RT

"

hconc ¼ RT 4F ln

PObulk 2 POTPB 2





exp , sca ¼ 4:210 T 7

PH2 O P

0:25

#

0:5

Reforming reaction rate (mol m3 sec1) Binary diffusion coefficient (m2 s1)

  cat exp  ERT " #

þ RT 2F ln

PHTPBO PHbulk 2

2

PHbulkO PHTPB 2

2

3  Rsr ¼ kþ MSR PCH4 PH2 O  kMSR PCO ðPH2 Þ

 Rsh ¼ kþ WGS PCO PH2 O  kWGS PCO2 PH2  1 2

0:001858 T 3=2

Knudsen diffusion coefficient (m2 s1) Effective gas diffusion coefficient (m2 s1) Ergun Equation (pressure drop)

1 þ M1 MA B

DAB ¼ Pv2AB UD qffiffiffiffiffi DKA ¼ 4850dpore MTA   AB * DKA DA;eff ¼ tε D DAB þDKA dP L

¼ A

mð1εÞ2 m ε3 D2p

m2

 Brð1εÞ ε3 D p

1200 T

  an exp  ERT

Table 6 Model equations for the calculation of internal steam reforming and diffusion of gas through porous media.

Shift reaction rate (mol m3 sec1)



10300 T



=

a

Anode electrode 6380 440 3.6 40 2.5 3.5 725



K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

649

Table 7 Governing equations for CFD calculations. Continuity

V$ ðruÞ ¼ Sr

Momentum

V$fðruÞug ¼ V$ðP þ m$VuÞ þ Sm

Energy

V$ðrCp uTÞ ¼ V$ ðkV$ TÞ þ Sh

Sr;ECRþRr ¼ SH2 þ SH2 O þ SCH4 þ SCO þ SCO2 Sr;cathode ¼ SO2  Sm ¼  Kmi ui þ 12Ci jujui ShECR ¼ ðT DSÞ$2FIse þ ðErev  VCell Þ$ ShReforming ¼ Rr Hr þ Rs Hs

Species

V$ðruYi Þ ¼ V$ðrDi;m V$Yi Þ þ Ssp

I 2F se

Hr ¼ ð206205:5 þ 19:5175TÞ Hs ¼ 45063  10:28T Sh ¼ ShECR þ ShReforming I M , S I Ssp;H2 ¼ 2F H2 SPcathode ¼ 4F MO2

SH2 ¼ SH2; ECR þ 3Rsr þ Rsh , SH2 O ¼ SH2; ECR  Rsr  Rsh SCH4 ¼ Rsr , SCO ¼ Rsr  Rsh , SCO2 ¼ Rsh

7. Stack simulation results In this section, results are discussed in terms of species mole fraction, temperature and current density distributions in the reaction layer. In the end, performance curves (I-V curve) of experiment and simulation are also presented. Fig. 7(a) shows mole fraction distributions of H2, CH4 and CO at the reaction surface of the stack with reference and developed manifolds. The mole fractions of all the reactant species are decreasing from the bottom of anode electrodes to the outlet on the top as these species are being consumed at anode-electrolyte interface and in porous anode electrode. Fig. 7(a)(i,iv) shows H2 mole fraction distribution for both manifold designs. In case of the stack with reference manifold, the indifferent molar concentration of hydrogen along the reaction surface for all the compartments is found which is highlighted in Fig. 7(a)(i). This localized depletion reflects that uneven H2 is being delivered by this manifold design to the anode channels. In comparison, fairly uniform H2 is distributed in case of the developed manifold. The localized mole fraction of hydrogen at the interface is varied from 0.4932 to 8.532e2 in the case of the stack with reference manifold whereas, in developed manifold stack, this variation is 0.4894 to 0.1188. This lowest concentration of H2 in the case of reference manifold stack, further support the claim made above for higher localized depletion of H2. In case of CH4 reforming reaction, the effect of flow uniformity is very small for first 40 cells, however, for the last 40 cells, a uniform reforming reaction on the reaction surface can be seen for the stack with the developed manifold. The effect of uniformity on ISR is marked in Fig. 7(a)(ii, v). The methane concentration was found as low as 7.552e5 in the case of reference manifold whereas for developed manifold the same is 1.414e4. However, larger variations have been observed in the case of CO shift reaction. As mentioned earlier that electrochemical oxidation of CO is neglected, only shift reaction is considered. The CO (17 mol %) is available in fuel stream and this act as a second source for the production of hydrogen. Its depletion profile from the bottom of the anode to the top outlet is closely linked with the CH4 reforming reaction because additional CO is being produced from this reaction. The effect of flow non-uniformity on the contours of CO is also quite apparent which is marked in Fig. 7(a)(iii). In contrast, CO distribution is relatively uniform in case of the developed manifold which is reflected in Fig. 7(a)(vi). The localized mole fraction of CO varied from 9.562e2 to 1.709e2 in the case of the stack with reference manifold whereas, in developed manifold stack, this variation is 9.452e2 to 2.386e2. The minimum concentration of CO of reference manifold stack signifies the non-uniform distributions and hence indifferent shift reaction at the interface surface. Fig. 7(b) shows distributions of pressure, temperature and current density in the stack with manifolds and at the reaction

surfaces. Fig. 7(b)(i, iv) shows a pressure drop comparison for reference and developed manifold stack designs respectively. The total pressure drop of 988 Pa and 960 Pa are observed for a stack with reference and developed manifolds design respectively. A higher pressure drop in the reference manifold stack is noted which further support the conclusions made in the previous section. Similar pressure drops across both the FT-SOFC's have been found. The pressure drops in the stack cells are mainly due to the viscous resistance of porous anode electrodes [8]. Lowering overall pressure drop is one of imperative constraint while designing the stack and achieving higher performance and steady operation [18]. Fig. 7(b)(ii, v) shows temperature distributions for both stack designs at the reaction surfaces. It is evident from figures that there are two distinct regions on the active surfaces; temperature is lowest at the bottom, whereas highest temperature is found at the top. The lowest temperature at the bottom is due to the fast endothermic reforming reaction; CH4 concentration depleted very quickly along the anode electrodes which can be seen in Fig. 7(b)(ii, v). In the downstream direction, heat produced by exothermic WGSR and irreversible electrochemical losses supersede the heat consumption by ISR [37e39]. This is the reason that higher temperatures are observed at the top. In the stack with reference manifold, there is a decrease in average surface temperature from first 40 cells to the last 40 cells which is highlighted in Fig. 7(b)(ii). Whereas, in the case of the stack with the developed manifold, temperature distributions in last 40 cells are considerably uniform from bottom to the top indicating a higher concentration of fuel is available to produce heat due to shift and electrochemical reactions. However, in the case of stack with reference manifold, the decline in temperature at the last 40 cells is due to the lower mass flow rate in the last 40 cells which can be seen in Fig. 4(a). Another noticeable point is the highest temperature region; this region is more towards the center of reaction surfaces for reference manifold stack than near the top of developed manifold stack which representing the better distribution of reacting species over the active surfaces. In addition, temperature distributions at the bottom of reaction surface for first 40 cells for both the manifold stacks differ considerably. A higher temperature at the bottom surfaces of first 40 cells of Fig. 7(b)(ii) indicates that lower concentration of CH4 is available for reforming reaction which further reveals the nonuniform distributions of reference manifold stack. Fig. 7(b)(iii, vi) shows local current density distributions at the reaction surfaces for both the stacks. The highest current density is observed at the point where both hydrogen and oxygen intersect and having highest partial pressures. Therefore, the current density is maximum at the bottom of reaction surfaces [3,20]. As the reactants are consumed in downstream, the current density is reduced along active surface [38]. The inconsistent current density distribution is seen in the case of the stack with reference manifold

650

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

Fig. 7. (a) The species distributions at the reaction surfaces of 80 cells stack with reference and developed manifolds. (b) The pressure, temperature and current distributions at the reaction surfaces of 80 cells stack with reference and developed manifolds.

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

651

Fig. 8. Performance curves (a) Model validation (stack with reference manifold) (b) Stack performance comparison between reference and developed manifold designs.

which are encircled in Fig. 7(b)(iii). This encircled current density is highest for first 40 cells due to the localized fast-reforming reaction in anode electrode generating more hydrogen. As discussed, the current density is greatly influenced by the partial pressures of hydrogen and oxygen. The oxygen utilization is around 20%, however, it is supplied in large excess to control the stack temperature. Thus, hydrogen distribution on the active surface is the major influencing factor for current density profile along with the temperature distribution due to the combination of exothermic electrochemical reactions and endothermic reforming reaction [40]. Therefore, the effect of species non-uniformity on the current density distributions is quite apparent for the stack with reference manifold. The current density distribution is rather uniform for the developed manifold stack, and the highest average current density of 3070 A m2 is achieved in comparison to 2999 A m2 for reference manifold stack. Fig. 8(a) compares I-V curves of an experimental and numerically simulated data of the stacks with reference manifold. The simulated results of the stack with reference manifold reveals a good agreement with the experimental results which validates the modeling used for full stack-scale simulation. The only difference is observed at the low current densities, indicating that physical property model for exchange current density exhibiting small error for this range [41]. The same validated ECR and ISR modeling are implemented for the numerical calculations of the stack with the developed manifold. A noticeable improvement in the stack voltage is observed for all electrical currents which is quite visible in Fig. 8(b). The maximum experimental stack power obtained at an electrical current of 19.08A is 1030.32W whereas this value for a stack with developed manifold under the same condition improves to 1110.46W. This increase in stack power along with the better flow uniformity and improved distributions of species, temperature, and current density shows that significant improvement has been achieved as a result of developed manifold design.

remodeled designs (b) linear tapering of cross section area of generic manifold (c) installing perforated sheet in the middle of manifold with variable holes sizes (d) remodeled manifold with diffuser with and without diffuser inlets (e) variable thickness of diffuser front. Stack flow uniformity and standard flow deviation indexes were utilized to investigate the flow uniformity among the different designs. The remodeled manifold without the diffuser inlets and 6 mm diffuser front exhibited the highest uniformity index and lowest flow deviation index at the stack and cell level among all tested manifold strategies. Furthermore, the developed manifold design exhibited a less pressure drop than the generic design. A full stack-scale simulations were also performed on the 80 cells FT-SOFC stack with the developed manifold by incorporating validated electrochemical and internal steam reforming reaction modeling of the stack with the generic manifold, and the effects of manifold designs on the performance of the stack were also elucidated. The significant improvements in the species, temperature, and current distributions have been achieved in the case of the stack with the developed manifold design. Also, an increase of ~8% stack power is achieved for a stack with developed manifold design in comparison to the experimental results performed on the stack with the generic manifold design. This manuscript provides a tool to evaluate quantitatively and compare degrees of flow distribution uniformity among the channels of FT-SOFC to optimize the manifold design. Acknowledgements The author gratefully appreciates the financial support of the Ministry of Trade, Industry & Energy (MOTIE) (Grant No. R0002207), and Korea Institute for Advancement of Technology (KIAT) and DaeGyeong Institute for Regional Program Evaluation (DGIRPE) through the Leading Industry Development for Economic Region. Nomenclature

8. Conclusions In this study, a comprehensive 3D numerical analysis has been performed to optimize the manifold design for a 1 kW-class flattubular solid oxide fuel cell (FT-SOFC) stack. The different manifold designs were suggested and detailed 3D numerical simulations were performed on the generic and as well as on the proposed designs. The geometric strategies that were systematically varied include: (a) variable manifold inlet diameters for both generic and

DAB DKA DA,eff Ean Eca E Erev

Binary diffusion coefficient of A and B, m2 s1 Knudsen diffusion coefficient of A, m2 s1 Effective diffusion coefficient of species A in gas mixture, m2 s1 Activation energy of anode, KJ mol1 Activation energy of cathode, KJ mol1 Standard state potential, V Reversible potential, V

652

F I P P Rirr Rsr Rsh Sr Sm Sh Ssp T Vcell

K. Rashid et al. / Journal of Power Sources 327 (2016) 638e652

Faraday constant, 96485.3 C mol1 Current density, A m2 Pressure, Pa Pressure at standard state, Pa Irreversible resistance, U m2 Rate of internal steam reforming reaction, mol m3 s1 Rate of water gas shift reaction, mol m3 s1 Source term in continuity equation, Kg m3 s1 Source term in momentum equation, Kg m2 s2 Source term in energy equation, W m3 Source term in species equation, Kg m3 s1 Temperature, K Cell voltage, V

Greek letters hconc Concentration over potential, V san Electronic conductivities of anode, U1 m1 sca Electronic conductivities of anode, U1 m1 se Ionic conductivities of electrolyte, U1 m1 m Fluid viscosity, Kg m1 s1 gan Pre-exponential factor of anode, A m2 gca Pre-exponential factor of cathode, A m2 Subscripts Bulk Bulk flow/flow through the anode channel Ract Activation overpotential at anode, U1 m2 an act Rca Activation overpotential at cathode, U1 m2 Rohm Ohmic over potential, U1 m2 TPB Triple phase boundary References [1] S.C. Singhal, K. Kendall, High Temperature and Solid Oxide Fuel Cells, Elsevier, New York, 2003. [2] B.H. Choi, I.W. Jang, H.J. Sung, Effects of microstructural functional layers on flat-tubular solid oxide fuel cells, Fuel Cells 13 (2013) 1088e1100. [3] J. Park, J. Bae, J.Y. Kim, A numerical study on anode thickness and channel diameter of anode-supported flat-tube solid oxide fuel cells, Renew. Energy 42 (2012) 180e185. [4] Y. Lu, L. Schaefer, P. Li, Numerical study of a flat-tube high power density solid oxide fuel cellPart I. Heat/mass transfer and fluid flow, J. Power Sources 140 (2005) 331e339. [5] D. Chen, Q. Zeng, S. Su, W. Bi, Z. Ren, Geometric optimization of a 10-cell modular planar solid oxide fuel cell stack manifold, Appl. Energy 112 (2013) 1100e1107. [6] J. Wang, Theory of flow distribution in manifolds, Chem. Eng. J. 168 (2011) 1331e1345. [7] H. Yakabe, M. Hishinuma, M. Uratani, Y. Matsuzaki, I. Yasuda, Evaluation and modeling of performance of anode-supported solid oxide fuel cell, J. Power Sources 86 (2000) 423e431. [8] R.T. Nishida, S.B. Beale, J.G. Pharoah, Impact of manifolding on performance of a solid oxide fuel cell stack, ECS Trans. 57 (2013) 2495e2504. [9] S. Su, H. He, D. Chen, W. Zhu, Y. Wu, W. Kong, et al., Flow distribution analyzing for the solid oxide fuel cell short stacks with rectangular and discrete cylindrical rib configurations, Int. J. Hydrogen Energy 40 (2015) 577e592. [10] R.J. Kee, P. Korada, K. Walters, M. Pavol, A generalized model of the flow distribution in channel networks of planar fuel cells, J. Power Sources 109 (2002) 148e159. [11] W. Bi, D. Chen, Z. Lin, A key geometric parameter for the flow uniformity in planar solid oxide fuel cell stacks, Int. J. Hydrogen Energy 34 (2009) 3873e3884.

[12] B. Lin, Y. Shi, M. Ni, N. Cai, Numerical investigation on impacts on fuel velocity distribution nonuniformity among solid oxide fuel cell unit channels, Int. J. Hydrogen Energy 40 (2015) 3035e3047. [13] R.J. Boersma, N.M. Sammes, Computational analysis of the gas flow distribution in solid oxide fuel cell stacks, J. Power Sources 63 (1996) 215e219. [14] C.M. Huang, S.S. Shy, C.H. Lee, On flow uniformity in various interconnects and its influence to cell performance of planar SOFC, J. Power Sources 183 (2008) 205e213. [15] W. Winkler, Influence of the mass transfer on the geometric design of SOFC stacks, J. Power Sources 86 (2000) 449e454. [16] W. Xia, Y. Yang, Q. Wang, Effects of operations and structural parameters on the one-cell stack performance of planar solid oxide fuel cell, J. Power Sources 194 (2009) 886e898. [17] Y. Sung, Optimization of a fuel-cell manifold, J. Power Sources 157 (2006) 395e400. [18] C.-H. Chen, S.-P. Jung, S.-C. Yen, Flow distribution in the manifold of PEM fuel cell stack, J. Power Sources 173 (2007) 249e263. [19] J.C.K. Tong, E.M. Sparrow, J.P. Abraham, Geometric strategies for attainment of identical outflows through all of the exit ports of a distribution manifold in a manifold system, Appl. Therm. Eng. 29 (2009) 3552e3560. [20] J. Park, J. Bae, Characterization of electrochemical reaction and thermo-fluid flow in metal-supported solid oxide fuel cell stacks with various manifold designs, Int. J. Hydrogen Energy 37 (2012) 1717e1730. [21] E. Achenbach, P. Costamagna, Fluid dynamic study of fuel cell devices: simulation and experimental validation, J. Power Sources 52 (1994) 243e249. [22] R.J. Boersma, N.M. Sammes, Distribution of gas flow in internally manifolded solid oxide fuel-cell stacks, J. Power Sources 66 (1997) 41e45. [23] J.H. Koh, H.K. Seo, C.G. Lee, Y.S. Yoo, H.C. Lim, Pressure and flow distribution in internal gas manifolds of a fuel-cell stack, J. Power Sources 115 (2003) 54e65. [24] K.P. Recknagle, R.E. Williford, L.A. Chick, D.R. Rector, M.A. Khaleel, Threedimensional thermo-fluid electrochemical modeling of planar SOFC stacks, J. Power Sources 113 (2003) 109e114. [25] N. Autissier, D. Larrain, J. Van Herle, D. Favrat, CFD simulation tool for solid oxide fuel cells, J. Power Sources 131 (2004) 313e319. [26] Y. Wang, F. Yoshiba, T. Watanabe, S. Weng, Numerical analysis of electrochemical characteristics and heat/species transport for planar porouselectrode-supported SOFC, J. Power Sources 170 (2007) 101e110. [27] R.P.O. Hayre, F.B. Prinz, Fuel Cell Fundamentals, John Wiley Sons, Inc, 2006. [28] A.F.T. Guide, Ansys Fluent Tutorial Guide. Ansys INC. 15.0 edition. [29] S. Mokhtari, V. Kudriavtsev, M. Danna, Flow uniformity and pressure variation in multi-outlet flow distribution pipes, ASME 355 (1997) 114e122. [30] J.M. Hassan, T.A. Mohamed, W.S. Mohammed, W.H. Alawee, Modeling the uniformity of manifold with various configurations, J. Fluids 2014 (2014) 1e8. [31] Y. Matsuzaki, I. Yasuda, Electrochemical oxidation of H2 and co in a H2-H2OCO-CO2 system at the interface of a Ni-YSZ cermet electrode and YSZ electrolyte, J. Electrochem. Soc. 147 (2000) 1630. [32] V.M. Janardhanan, O. Deutschmann, Numerical study of mass and heat transport in solid-oxide fuel cells running on humidified methane, Chem. Eng. Sci. 62 (2007) 5473e5486. [33] P. Costamagna, Modeling of solid oxide heat exchanger integrated stacks and simulation at high fuel utilization, J. Electrochem. Soc. 145 (1998) 3995. [34] M. Suzuki, M. Suzuki, N. Shikazono, N. Shikazono, K. Fukagata, K. Fukagata, et al., Numerical analysis of coupled transport and reaction phenomena in an anode-supported flat-tube solid oxide fuel cell, J. Power Sources 40 (2008) 29e40. [35] W. Lehnert, J. Meusinger, F. Thom, Modelling of gas transport phenomenan in SOFC anodes, J. Power Sources 87 (2000) 57e63. [36] J.R. Welty, C.E. Wicks, R.E. Wilson, G.L. Rorrer, Fundamentals of Momentum, Heat, and Mass Transfer, fifth ed., John Wiley Sons, Inc, 2007. [37] M. Ni, Modeling of SOFC running on partially pre-reformed gas mixture, Int. J. Hydrogen Energy 37 (2012) 1731e1745. [38] K. Fischer, J.R. Seume, Location and magnitude of heat sources in solid oxide fuel cells, J. Fuel Cell Sci. Technol. 6 (2009) 011002. [39] B.A. Haberman, J.B. Young, Three-dimensional simulation of chemically reacting gas flows in the porous support structure of an integrated-planar solid oxide fuel cell, Int. J. Heat. Mass Transf. 47 (2004) 3617e3629. [40] Y.J. Kim, I.G. Chang, T.W. Lee, M.K. Chung, Effects of relative gas flow direction in the anode and cathode on the performance characteristics of a Molten Carbonate Fuel Cell, Fuel 89 (2010) 1019e1028. [41] J. Park, Y.M. Kim, J. Bae, Electrochemical simulation using material properties of a ceramic electrode and electrolyte, Curr. Appl. Phys. 11 (2011) S219eS222.